352 Analysis of Scientific Books and Memoirs. 



veral results obtained by these writers, for beams of all forms and dimen- 

 sions- These, as we have before stated, differ essentially from each other, 

 when the results are made dependent on the strength of direct cohesion, 

 although with similar formed beams, and under similar circumstances, the 

 proportions deduced from each are the same. 



One of the most remarkable differences in these deductions is, that, ad- 

 mitting the law of Galileo, which is equivalent to making v=o, an equila- 

 teral triangular beam will be twice as strong, broken with its edge down- 

 wards, as when reversed, so as to make the base the fulcrum of motion, 

 the edge leaning upwards. And, according to Leibnitz, the proportions 

 of strength in the two cases is as 1 to 3 ; whereas, by experiments report- 

 ed by Mr Barlow, it appears that the strength in the two cases is nearly 

 equal, what difference there is, being on the opposite side to that deduced 

 from theory. From this, therefore, it is demonstrated, as was before as- 

 serted by Coulomb, Dr Robison, and others, that both hypotheses are erro- 

 neous, the errors in each arising from considering the material as incom- 

 pressible, and thereby supposing the beam to turn about its lower edge, 

 whereas, in fact, it is partly compressed, and partly extended, the motion 

 being about an intermediate line, now commonly denominated the neutral 

 axis, because the fibre, situated at this place, is supposed to be neither ex- 

 tended nor compressed. The investigation of this question is the next ob- 

 ject of the author, who, adopting the theory of Coulomb and Dr Robison, 

 arrives at this formula : 



i u • *,► — TXD + TX a 



breaking weight = ^ — 



Where T ==, the sum of the forces arising from tension, D and a, the dis- 

 tance of the centres of tensions, and compression from the neutral axis, 

 L, the length of the beam, and C, the cosine of its deflection ; and here we 

 fall upon the principal question, arising out of the paper under review, 

 viz. the theory of Coulomb, Hodgkinson, and others, versus Barlow's. 

 It is not our intention to give any decision on this subject, but we shall 

 endeavour to lay the question fairly before our readers, and leave them, or 

 those most practically conversant with these subjects, to decide, in order 

 to do which, however, we must quote at some length from the Memoir in 

 question. 



After showing, as we have done above, that there must be in the beam 

 a certain neutral line, Mr H. proceeds. 



" If then, in Plate II. Fig. 4, (given in last Number,) in which adbc 

 is intended to represent the surface of fracture, ah be the neutral line, or 

 that of which we have been speaking, and it aid be the surface of extension 

 and acb that of compression, it is evident that the extensions, or compres- 

 sions of any particles, within those surfaces, will be as their distances from 

 the line ab ; and the forces necessary to produce them may be considered 

 as in proportion to some powers v and to of those distances. 



And in order to estimate the strength of the piece, whose section is acbd, 

 if F and /represent the points at which the forces, rising from extension 

 and compression, being collected, would produce the same effects as they 

 do at their respective distances from the neutral line : f will be the ful- 

 crum, on which all the horizontal forces may be conceived as sustained, 



